Krylov Subspace Methods for Linear Systems, Eigenvalues and Model Order Reduction
New variants of Krylov subspace methods for numerical solution of linear systems, eigenvalue, and model order reduction problems are described.
A new method to solve linear systems of equations with several right-hand sides is described. It uses the basis from a previous solution to reduce the number of matrix vector multiplications needed to solve a linear system of equations with a new right-hand side.
For eigenproblems and model order reduction the rational Krylov method is used. The rational Krylov method is an extension of the shift-and-invert Arnoldi method where several shifts (factorisations of a shifted pencil) are used to compute an orthonormal basis for a subspace. It is shown how the basis vectors can be generated in parallel. It is also shown how to create a reduced-order model of a linear dynamic system, and how to make error estimates of the Laplace domain transfer function of the reduced-order model. Further it is shown how to make a passive model of a passive RLC circuit.
AMS subject classification 65F15, 65F50, 65Y05, 65F10, 93A30, 93B40